Representations of finite special linear groups in non-defining characteristic

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170754We determine precisely the number of irreducible summands of an irreducible cross characteristic representation of $GL_{n}(q)$ on restriction to $SL_{n}(q)$. Combined with a recent result of C. Bonnafe, this yields a canonical labeling for irreducible $\ell$-modular representations of $SL_{n}(q)$, where $(\ell,q)=1$. As an application, we classify for the first time complex representations of $SL_{n}(q)$ whose reductions modulo $\ell$ are irreducible.24 pages. Advances in Mathematics, to appearRepresentation TheoryGroup Theory20C20, 20E28, 20G40Representations of finite special linear groups in non-defining characteristictext